Lab 3: CNN Visualization¶
Group Members:
Parker Brown
Suma Chackola
Chris Peters
Oliver Raney
The execution of this lab was performed collaboratively across 4 computers. Therefore, while the individual cells are not all shown with the direct execution results, the code presented in those cells was utilized to produce the results in this notebook.
In this lab we will find and analyze a circuit in a common neural network. A reference figure is also shown to help clarify the process of finding and analyzing deep circuits.
The terminology used in this lab is as follows:
- (1) a filter refers to the entire tensor that convolves with an input across all channels (i.e., a multi-channel filter like a 3x3x64 tensor)
- (2) a single channel filter refers to one channel of the aforementioned filter (e.g., a 3x3x1 convolution kernel)
- (3) and activation refers to the input or output of the filter depending on context (i.e., input activations for a filter are the outputs from a previous layer, output activations are all the filter outputs from a convolutional layer)
- (4) an input can refer to all input channels or a single input channel depending on the context (entire filter or single channel filter, respectively).
A diagram is provided for clarity and this was covered in detail in the class lecture.
In [1]:
from IPython.display import Image
Image(filename='CircuitsFigure.png')
Out[1]:
1.0 Introduction & CNN Overview¶
VGG19 is a deep convolutional neural network architecture that is widely used for various computer vision tasks, including image classification and object detection. We are using the VGG19 architecture that is built into keras.
We chose to utilize VGG19 for this lab because of its simple architecture and its accessibility for pre-trained weights (ImageNet in this case). The network consists of 19 layers, including multiple convolutional layers and fully connected layers. These layers capture hierarchical features of an input image, making it suitable for visualizing the learned representations in a CNN.
By visualizing the activations of different layers in VGG19, we hope to gain insights into how the network processes and understands images. This can help in understanding the inner workings of the network and identifying important features.
Data Source¶
Below, we will first use a pre-labeled image dataset to measure VGG19's performance before altering any layers. The dataset comes from Kaggle and contains 45 different classes of images that are 256x256 in size, with around 300 samples per class. We chose to use 10 of the 45 available classes. https://www.kaggle.com/datasets/asaniczka/mammals-image-classification-dataset-45-animals
In [2]:
import numpy as np
import matplotlib.pyplot as plt
from keras.applications import VGG19
from keras.applications.vgg19 import preprocess_input, decode_predictions
#from keras.preprocessing.image import load_img, img_to_array
from keras.preprocessing import image
from keras.utils import load_img, img_to_array
model = VGG19(weights='imagenet')
#model = VGG19(weights='imagenet', include_top=False, input_tensor=None)
def predict_and_plot(image_path):
# Load the image
img = load_img(image_path, target_size=(224, 224))
img = img_to_array(img)
img = np.expand_dims(img, axis=0)
img = preprocess_input(img)
# Predict the image
predictions = model.predict(img)
predicted_label = decode_predictions(predictions, top=1)[0][0]
# Plot the image
plt.figure()
plt.imshow(plt.imread(image_path))
#TODO: Need to check why this is giving errors
#plt.title(f'{predicted_label[1]} ({predicted_label[2]:.2f})')
print(f'{predicted_label[1]} ({predicted_label[2]:.2f})')
plt.axis('off')
plt.show()
In [3]:
predict_and_plot('mammals/african_elephant/african_elephant-0006.jpg')
predict_and_plot('mammals/camel/camel-0003.jpg')
predict_and_plot('mammals/brown_bear/brown_bear-0002.jpg')
predict_and_plot('mammals/giraffe/giraffe-0024.jpg')
predict_and_plot('mammals/zebra/zebra-0092.jpg')
1/1 [==============================] - 0s 280ms/step African_elephant (0.78)
1/1 [==============================] - 0s 95ms/step Arabian_camel (1.00)
1/1 [==============================] - 0s 83ms/step brown_bear (0.94)
1/1 [==============================] - 0s 87ms/step gazelle (0.73)
1/1 [==============================] - 0s 95ms/step zebra (1.00)
2.0 Circuit Selection & Extraction Hypothesis¶
[4 points]
Select a multi-channel filter (i.e., a feature) in a layer in which to analyze as part of a circuit. This should be a multi-channel filter in a "mid-level" portion of the network (that is, there are convolutional layers before and after this chosen layer). You might find using OpenAI microscope a helpful tool for selecting a filter to analyze without writing too much code:¶
https://microscope.openai.com/models/
- Using image gradient techniques, find an input image that maximally excites this chosen multi-channel filter. General techniques are available from class:¶
https://github.com/8000net/LectureNotesMaster/blob/master/04%20LectureVisualizingConvnets.ipynb
- Also send images of varying class (i.e., from ImageNet) through the network and track which classes of images most excite your chosen filter.¶
- Give a hypothesis for what this multi-channel filter might be extracting. That is, what do you think its function is in the network? Give reasoning for your hypothesis.¶
- If using code from another source or a LLM, you should heavily document the code so that I can grade your understanding of the code used.¶
Source:¶
In our approach, we are utilizing the code available in Dr. Larson's Notebook "04 LectureVisualizingConvnets", which utilizes Ian Stenbit's code from Francois Chollet's notebook: https://github.com/fchollet/deep-learning-with-python-notebooks/. We tailored the code to our specific CNN and filters, but in general the code is mostly the same.
Our approach is the following:
- Select a filter from Open AI microscope
- Utilize gradient ascent techniques from example notebook to analyze input image, starting with noisy image
- Analyze filter with images of varying classes to determine which classes are most excitatory
In [1]:
# watermark the notebook
import os
os.environ['TF_CPP_MIN_LOG_LEVEL'] = '3'
import sys
import tensorflow.keras
import scipy as sp
import tensorflow as tf
import platform
import numpy as np
import matplotlib.pyplot as plt
print(f"Python Platform: {platform.platform()}")
print(f"Tensor Flow Version: {tf.__version__}")
print(f"Keras Version: {tensorflow.keras.__version__}")
print()
print(f"Python {sys.version}")
gpus = tf.config.list_physical_devices('GPU')
print("GPU Resources Available:\n\t",gpus)
# getting rid of the warning messages about optimizer graph
tf.get_logger().setLevel('ERROR')
tf.autograph.set_verbosity(3)
Python Platform: Windows-10-10.0.22631-SP0 Tensor Flow Version: 2.10.1 Keras Version: 2.10.0 Python 3.8.18 (default, Sep 11 2023, 13:39:12) [MSC v.1916 64 bit (AMD64)] GPU Resources Available: []
In [5]:
#From lecture 04
# We preprocess the image into a 4D tensor
def prepare_image_for_display(img, norm_type='max'):
if norm_type == 'max':
# min/max scaling, best for regular images
new_img = (img - img.min()) / (img.max()-img.min())
else:
# std scaling, best when we are unsure about large outliers
new_img = ((img - img.mean()) / (img.std() +1e-3))*0.15 + 0.5
new_img *= 255
new_img = np.clip(new_img, 0, 255)
if len(new_img.shape)>3:
new_img = np.squeeze(new_img)
return new_img.astype('uint8')
In [6]:
# let's look at the model for VGG
model = VGG19(weights='imagenet', include_top=False, input_tensor=None)
model.summary()
Model: "vgg19"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
input_2 (InputLayer) [(None, None, None, 3)] 0
block1_conv1 (Conv2D) (None, None, None, 64) 1792
block1_conv2 (Conv2D) (None, None, None, 64) 36928
block1_pool (MaxPooling2D) (None, None, None, 64) 0
block2_conv1 (Conv2D) (None, None, None, 128) 73856
block2_conv2 (Conv2D) (None, None, None, 128) 147584
block2_pool (MaxPooling2D) (None, None, None, 128) 0
block3_conv1 (Conv2D) (None, None, None, 256) 295168
block3_conv2 (Conv2D) (None, None, None, 256) 590080
block3_conv3 (Conv2D) (None, None, None, 256) 590080
block3_conv4 (Conv2D) (None, None, None, 256) 590080
block3_pool (MaxPooling2D) (None, None, None, 256) 0
block4_conv1 (Conv2D) (None, None, None, 512) 1180160
block4_conv2 (Conv2D) (None, None, None, 512) 2359808
block4_conv3 (Conv2D) (None, None, None, 512) 2359808
block4_conv4 (Conv2D) (None, None, None, 512) 2359808
block4_pool (MaxPooling2D) (None, None, None, 512) 0
block5_conv1 (Conv2D) (None, None, None, 512) 2359808
block5_conv2 (Conv2D) (None, None, None, 512) 2359808
block5_conv3 (Conv2D) (None, None, None, 512) 2359808
block5_conv4 (Conv2D) (None, None, None, 512) 2359808
block5_pool (MaxPooling2D) (None, None, None, 512) 0
=================================================================
Total params: 20024384 (76.39 MB)
Trainable params: 20024384 (76.39 MB)
Non-trainable params: 0 (0.00 Byte)
_________________________________________________________________
We went to OpenAI to find a filter to analyze. The below output is for VGG19, Block 5, Convolution 2, Filter 179 (https://microscope.openai.com/models/vgg19_caffe/conv5_2_conv5_2_0/179)
Looking at OpenAI microscope, we can see that lots of input images from ImageNet are dogs with a vertical line of white fur on their faces. This may be related to how the Zebra class, which has white lines, is the highest average value for the activation.
The reason we chose this one is because it seems to be biased to eyes and face shapes, especially when in the presence of stripes and strong color distinctions. Our dataset contains images of zebras & giraffes, which have those shapes as prominent, distinguishing features.
In [9]:
Image(filename='OpenAI_Filter_block5_conv2_filter_179.png')
Out[9]:
In [7]:
from keras import models
# set VGG to be frozen
for layer in model.layers:
layer.trainable = False
# Selecting a layer and channel to visualize
layer_name = 'block5_conv2'
filter_index = 100
# Isolate the output of interest and create new model
layer_output = model.get_layer(layer_name).output
new_model = models.Model(inputs=model.input, outputs=layer_output)
# now "new_model" has the output we desire to maximize
# create a variable that we can access and update in computation graph
I = tf.Variable(np.zeros((1, 150, 150, 3),dtype='double'), name='image_var', dtype = 'float64')
# now use gradient tape to get the gradients (watching only the variable v)
with tf.GradientTape(watch_accessed_variables=False) as tape:
tape.watch(I) # watch
model_vals = new_model(preprocess_input(I)) # get output
filter_output_to_maximize = tf.reduce_mean(model_vals[:, :, :, filter_index]) # define what we want to maximize
grad_fn = tape.gradient(filter_output_to_maximize, I) # get gradients that influence loss w.r.t. v
grad_fn /= (tf.sqrt(tf.reduce_mean(tf.square(grad_fn))) + 1e-5) # mean L2 norm (better stability)
# now show the gradient, same size as input image
plt.imshow(prepare_image_for_display( grad_fn.numpy(), norm_type='std'))
#plt.title('The gradient of filter w.r.t I, $ \sum\partial f_n(I)_{i,j} $ ')
plt.show()
The focus of that output appears to be in the bottom left half of the image for higher what appears to be some higher frequency detail.
In [8]:
#Using gradient ascent
def generate_pattern(layer_name, filter_index, size=150):
# Build a model that outputs the activation
# of the nth filter of the layer considered.
layer_output = model.get_layer(layer_name).output
# Isolate the output
new_model = models.Model(inputs=model.input, outputs=layer_output)
# We start from a gray image with some uniform noise
input_img_data = np.random.random((1, size, size, 3)) * 20 + 128.
I_start = tf.Variable(input_img_data, name='image_var', dtype = 'float64')
I = preprocess_input(I_start) # only process once
# Run gradient ascent for 40 steps
eta = 1.
for i in range(40):
with tf.GradientTape(watch_accessed_variables=False) as tape:
tape.watch(I)
# get variable to maximize
model_vals = new_model(I)
filter_output = tf.reduce_mean(model_vals[:, :, :, filter_index])
# Compute the gradient of the input picture w.r.t. this loss
# add this operation input to maximize
grad_fn = tape.gradient(filter_output, I)
# Normalization trick: we normalize the gradient
grad_fn /= (tf.sqrt(tf.reduce_mean(tf.square(grad_fn))) + 1e-5) # mean L2 norm
I += grad_fn * eta # one iteration of maximizing
# return the numpy matrix so we can visualize
img = I.numpy()
return prepare_image_for_display(img, norm_type='std')
In [10]:
#This is the chosen filter we are going to use through the rest of this notebook
chosen_filter=179
In [11]:
#SHow the chosen filter pattern
plt.imshow(generate_pattern('block5_conv2', chosen_filter))
plt.show()
This seems to indicate some areas of blurring and some areas of high density.
In [12]:
#Looking at some more patterns and the variety that is evident
for layer_name in ['block5_conv2']:
size = 64
margin = 5
# This a empty (black) image where we will store our results.
results = np.zeros((8 * size + 7 * margin, 8 * size + 7 * margin, 3)).astype('uint8')
for i in range(8): # iterate over the rows of our results grid
for j in range(8): # iterate over the columns of our results grid
# Generate the pattern for filter `i + (j * 8)` in `layer_name`
filter_img = generate_pattern(layer_name, i + (j * 8), size=size)
# Put the result in the square `(i, j)` of the results grid
horizontal_start = i * size + i * margin
horizontal_end = horizontal_start + size
vertical_start = j * size + j * margin
vertical_end = vertical_start + size
results[horizontal_start: horizontal_end, vertical_start: vertical_end, :] = filter_img
# Display the results grid
plt.figure(figsize=(20, 20))
plt.imshow(results)
#plt.title(layer_name)
plt.show()
In [13]:
keras_layer = new_model.get_layer(layer_name)
layer_output = keras_layer.output
weights_list = keras_layer.get_weights() # list of filter, the biases
filters = weights_list[0]
biases = weights_list[1]
# print out some specifics of how the filter is saved
print(layer_name, ' activation size is ', layer_output.get_shape(), '(batch x H x W x filter)')
print(layer_name, ' filters is of shape',filters.shape, '...(k x k x channels x filters)')
print(layer_name, ' biases is of shape',biases.shape)
block5_conv2 activation size is (None, None, None, 512) (batch x H x W x filter) block5_conv2 filters is of shape (3, 3, 512, 512) ...(k x k x channels x filters) block5_conv2 biases is of shape (512,)
In [14]:
#To display what preprocess does to the image
path_to_image = 'mammals/african_elephant/african_elephant-0001.jpg' #Animals/raw-img/cane/OIP-_3acmW_iSr12XgQTNz0IdQHaFj.jpeg'
img = load_img(path_to_image, target_size=(512,512))
img = img_to_array(img)
img = np.expand_dims(img, axis=0)
img_prepped = preprocess_input(img)
print('Preprocessed')
plt.subplot(1,2,1)
plt.imshow(prepare_image_for_display(img_prepped))
plt.show()
Preprocessed
In [15]:
#Checking the dimensions :)
img_prepped.shape
Out[15]:
(1, 512, 512, 3)
In [16]:
# Some helper functions
import os
import seaborn as sns
directory = 'mammals'
n_cols = 5
n_rows = 2
size = 512
index = 0
def get_one_per_class():
titles = []
# iterate over files and folders in that directory
for path, folders, files in os.walk(directory):
for folder_name in folders:
folder_path = path+'/'+folder_name
image_name = os.listdir(folder_path)[0]
path_to_image = folder_path +'/'+image_name
#print(path_to_image)
titles.append(path_to_image)
return titles
def get_all_in_class(classpath):
titles = []
# iterate over files and folders in that directory
for root, subdolders, files in os.walk(classpath):
for filename in files:
img_path = os.path.join(root, filename)
#print(img_path)
titles.append(img_path)
return titles
In [20]:
def get_activations(path_to_image):
img = load_img(path_to_image, target_size=(512,512))
img = img_to_array(img)
img = np.expand_dims(img, axis=0)
img_prepped = preprocess_input(img)
activations = new_model.predict(img_prepped)
return activations
activations =get_activations(titles[9])
activations.shape
1/1 [==============================] - 0s 235ms/step
Out[20]:
(1, 32, 32, 512)
In [19]:
def show_chosen_filter(activations, titlef, idx_filter=408, show_original = True):
one_channel = activations[0, :, :, idx_filter] # get single activation channel
plt.figure(figsize=(2,1))
plt.title = titlef
plt.subplot(1,2,1)
plt.imshow(prepare_image_for_display(one_channel, norm_type = 'std'))
plt.subplot(1,2,2)
if show_original == True:
plt.imshow(plt.imread(titlef))
plt.show()
show_chosen_filter(activations, titles[9],chosen_filter)
In [21]:
#for the chosen filter pass through the titles shown earlier
titles = get_one_per_class()
for title in titles:
print(title)
activations =get_activations(title)
show_chosen_filter(activations, title, chosen_filter)
mammals/african_elephant/african_elephant-0001.jpg 1/1 [==============================] - 0s 233ms/step
mammals/brown_bear/brown_bear-0001.jpg 1/1 [==============================] - 0s 255ms/step
mammals/camel/camel-0001.jpg 1/1 [==============================] - 0s 237ms/step
mammals/dolphin/dolphin-0001.jpg 1/1 [==============================] - 0s 227ms/step
mammals/giraffe/giraffe-0001.jpg 1/1 [==============================] - 0s 252ms/step
mammals/horse/horse-0001.jpg 1/1 [==============================] - 0s 237ms/step
mammals/koala/koala-0001.jpg 1/1 [==============================] - 0s 230ms/step
mammals/opossum/opossum-0001.jpg 1/1 [==============================] - 0s 237ms/step
mammals/rhinoceros/rhinoceros-0001.jpg 1/1 [==============================] - 0s 226ms/step
mammals/zebra/zebra-0001.jpg 1/1 [==============================] - 0s 228ms/step
In [22]:
# Now let's display our feature maps (the activations variable is from the model.predict above)
#From the lecture notes
import keras
images_per_row = 10
# This is the number of features in the feature map
n_features = activations.shape[-1]
# The feature map has shape (1, size, size, n_features)
size = activations.shape[1] #512
# We will tile the activation channels in this matrix
n_cols = n_features // images_per_row
display_grid = np.zeros((size * n_cols, images_per_row * size))
# We'll tile each filter into this big horizontal grid
for col in range(n_cols):
for row in range(images_per_row):
channel_image = activations[0,
:, :,
col * images_per_row + row]
# Post-process the feature to make it visually palatable
channel_image = prepare_image_for_display(channel_image,
norm_type = 'std')
display_grid[col * size : (col + 1) * size,
row * size : (row + 1) * size] = channel_image
# Display the grid
scale = 1. / size
plt.figure(figsize=(scale * display_grid.shape[1],
scale * display_grid.shape[0]))
#plt.title(layer_name)
plt.grid(False)
plt.imshow(display_grid, aspect='auto', cmap='viridis')
plt.show()
This filter seems to be extracting features related to stripes and strong color distinctions. Our dataset contains images of zebras & giraffes, which have those shapes as prominent, distinguishing features.
L1 Norm¶
We analyzed the L1 Norm, which is the sum of the magnitudes of the vectors. This norm weights all vectors equally.
In [23]:
# Also send images of varying class (i.e., from ImageNet) through the network
# and track which classes of images most excite your chosen filter.
def get_L1values_for_class(idx_filter, class_path):
class_L1s =[]
titles = get_all_in_class(class_path)
for title in titles:
class_activations = get_activations(title)
chosen_channel = class_activations[0, :, :, idx_filter]
L1_val = np.sum(np.abs(chosen_channel))
class_L1s.append(L1_val)
return class_L1s
#TODO: Feel free to replace with L2 instead of L1
def compile_L1stats_per_class( idx_filter, directory='mammals'):
class_paths=[]
class_maxL1s=[]
class_avgL1s=[]
class_L1s =[]
for root, subfolders, files in os.walk(directory):
for subfolder in subfolders:
class_path = os.path.join(root, subfolder)
print(class_path, "..fetching L1 stats for this class")
class_paths.append(class_path)
class_L1s = get_L1values_for_class( idx_filter, class_path)
#maxL1_idx = np.argsort(class_L1s)[-1:]
class_maxL1s.append(np.max(class_L1s))
avgL1 = np.average(class_L1s)
class_avgL1s.append(avgL1)
return class_paths, class_maxL1s, class_avgL1s
In [25]:
# test for one class first
results = get_L1values_for_class(chosen_filter, 'mammals\zebra')
print(results)
1/1 [==============================] - 0s 253ms/step 1/1 [==============================] - 0s 225ms/step 1/1 [==============================] - 0s 234ms/step 1/1 [==============================] - 0s 239ms/step 1/1 [==============================] - 0s 247ms/step 1/1 [==============================] - 0s 232ms/step 1/1 [==============================] - 0s 227ms/step 1/1 [==============================] - 0s 229ms/step 1/1 [==============================] - 0s 246ms/step 1/1 [==============================] - 0s 253ms/step 1/1 [==============================] - 0s 260ms/step 1/1 [==============================] - 0s 237ms/step 1/1 [==============================] - 0s 229ms/step 1/1 [==============================] - 0s 225ms/step 1/1 [==============================] - 0s 231ms/step 1/1 [==============================] - 0s 228ms/step 1/1 [==============================] - 0s 233ms/step 1/1 [==============================] - 0s 230ms/step 1/1 [==============================] - 0s 239ms/step 1/1 [==============================] - 0s 236ms/step 1/1 [==============================] - 0s 245ms/step 1/1 [==============================] - 0s 228ms/step 1/1 [==============================] - 0s 238ms/step 1/1 [==============================] - 0s 232ms/step 1/1 [==============================] - 0s 239ms/step 1/1 [==============================] - 0s 225ms/step 1/1 [==============================] - 0s 232ms/step 1/1 [==============================] - 0s 249ms/step 1/1 [==============================] - 0s 236ms/step 1/1 [==============================] - 0s 234ms/step 1/1 [==============================] - 0s 229ms/step 1/1 [==============================] - 0s 251ms/step 1/1 [==============================] - 0s 234ms/step 1/1 [==============================] - 0s 227ms/step 1/1 [==============================] - 0s 253ms/step 1/1 [==============================] - 0s 239ms/step 1/1 [==============================] - 0s 230ms/step 1/1 [==============================] - 0s 230ms/step 1/1 [==============================] - 0s 231ms/step 1/1 [==============================] - 0s 239ms/step 1/1 [==============================] - 0s 245ms/step 1/1 [==============================] - 0s 262ms/step 1/1 [==============================] - 0s 396ms/step 1/1 [==============================] - 0s 292ms/step 1/1 [==============================] - 0s 267ms/step 1/1 [==============================] - 0s 271ms/step 1/1 [==============================] - 0s 246ms/step 1/1 [==============================] - 0s 233ms/step 1/1 [==============================] - 0s 227ms/step 1/1 [==============================] - 0s 232ms/step 1/1 [==============================] - 0s 235ms/step 1/1 [==============================] - 0s 226ms/step 1/1 [==============================] - 0s 225ms/step 1/1 [==============================] - 0s 236ms/step 1/1 [==============================] - 0s 253ms/step 1/1 [==============================] - 0s 251ms/step 1/1 [==============================] - 0s 242ms/step 1/1 [==============================] - 0s 252ms/step 1/1 [==============================] - 0s 240ms/step 1/1 [==============================] - 0s 244ms/step 1/1 [==============================] - 0s 248ms/step 1/1 [==============================] - 0s 243ms/step 1/1 [==============================] - 0s 276ms/step 1/1 [==============================] - 0s 259ms/step 1/1 [==============================] - 0s 245ms/step 1/1 [==============================] - 0s 233ms/step 1/1 [==============================] - 0s 247ms/step 1/1 [==============================] - 0s 253ms/step 1/1 [==============================] - 0s 267ms/step 1/1 [==============================] - 0s 254ms/step 1/1 [==============================] - 0s 238ms/step 1/1 [==============================] - 0s 247ms/step 1/1 [==============================] - 0s 246ms/step 1/1 [==============================] - 0s 238ms/step 1/1 [==============================] - 0s 240ms/step 1/1 [==============================] - 0s 277ms/step 1/1 [==============================] - 0s 239ms/step 1/1 [==============================] - 0s 240ms/step 1/1 [==============================] - 0s 243ms/step 1/1 [==============================] - 0s 231ms/step 1/1 [==============================] - 0s 255ms/step 1/1 [==============================] - 0s 255ms/step 1/1 [==============================] - 0s 261ms/step 1/1 [==============================] - 0s 263ms/step 1/1 [==============================] - 0s 276ms/step 1/1 [==============================] - 0s 297ms/step 1/1 [==============================] - 0s 257ms/step 1/1 [==============================] - 0s 254ms/step 1/1 [==============================] - 0s 234ms/step 1/1 [==============================] - 0s 240ms/step 1/1 [==============================] - 0s 233ms/step 1/1 [==============================] - 0s 243ms/step 1/1 [==============================] - 0s 240ms/step 1/1 [==============================] - 0s 233ms/step 1/1 [==============================] - 0s 229ms/step 1/1 [==============================] - 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In [26]:
#for all the classes, get the L1 stats.
classes, class_max, class_avg = compile_L1stats_per_class(chosen_filter, 'mammals')
mammals\african_elephant ..fetching L1 stats for this class 1/1 [==============================] - 0s 238ms/step 1/1 [==============================] - 0s 235ms/step 1/1 [==============================] - 0s 231ms/step 1/1 [==============================] - 0s 232ms/step 1/1 [==============================] - 0s 228ms/step 1/1 [==============================] - 0s 231ms/step 1/1 [==============================] - 0s 231ms/step 1/1 [==============================] - 0s 232ms/step 1/1 [==============================] - 0s 230ms/step 1/1 [==============================] - 0s 232ms/step 1/1 [==============================] - 0s 236ms/step 1/1 [==============================] - 0s 230ms/step 1/1 [==============================] - 0s 230ms/step 1/1 [==============================] - 0s 228ms/step 1/1 [==============================] - 0s 234ms/step 1/1 [==============================] - 0s 231ms/step 1/1 [==============================] - 0s 235ms/step 1/1 [==============================] - 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In [27]:
#Display the results
idx = 0
for class_name in classes:
print('Class: ', class_name, ", L1 Max: ", class_max[idx], ', L1 avg:', class_avg[idx] )
idx+=1
Class: mammals\african_elephant , L1 Max: 43121.715 , L1 avg: 12058.041 Class: mammals\brown_bear , L1 Max: 34281.953 , L1 avg: 12205.884 Class: mammals\camel , L1 Max: 47433.24 , L1 avg: 10280.068 Class: mammals\dolphin , L1 Max: 32535.475 , L1 avg: 3873.0928 Class: mammals\giraffe , L1 Max: 42767.516 , L1 avg: 9540.603 Class: mammals\horse , L1 Max: 36893.258 , L1 avg: 11822.569 Class: mammals\koala , L1 Max: 48610.242 , L1 avg: 8040.6543 Class: mammals\opossum , L1 Max: 23742.648 , L1 avg: 7544.084 Class: mammals\rhinoceros , L1 Max: 27329.367 , L1 avg: 7308.498 Class: mammals\zebra , L1 Max: 54525.984 , L1 avg: 14256.438
Summary¶
We chose filter 179 from block5_conv2 of VGG19. This filter seems to be extracting features related to stripes and strong color distinctions. Our dataset contains images of zebras & giraffes, which have those shapes as prominent, distinguishing features.
When we saved the output activations for the chosen filter and summed them, Zebra has the max value for the activation. Further, as predicted, it has the highest avarage value. This was as expected when we picked that filter from Open AI images, because the filter seems to be biased to shapes prominent in zebras. However, the next largest are the elephant and the brown bear.
3.0 Circuit Analysis¶
[4 points]
Analyze each channel of the multi-channel filter to better understand how this might form a circuit (i.e., the weights of the filter). That is, visualize the convolutional filter (one channel at a time) between the input activations and the current activation to understand which inputs make up a circuit. You should avoid filter channels that are mostly "zero" coefficients. These are not influential for the circuit. One method of doing this is given below:¶
- Extract the filter coefficients for each input activation to that multi-channel filter. Note: If the multi-channel filter is 5x5 with an input channel size of 64, then this extraction will result in 64 different single channel filters, each of size 5x5.¶
- Keep the top ten sets of inputs with the "strongest" weights. For now, you can use the L2 norm of each input filter as a measure of strength. Visualize these top ten filters.¶
- For these ten strongest input filters, categorize each as "mostly inhibitory" or "mostly excitatory." That is, does each filter consist of mostly negative or mostly positive coefficients?¶
Process:¶
For this section, we are analyzing filter 179 in block5_conv2. We will extract the individual channels and visualize them. We will then determine their strengths by summing their weights. We will classify the weights as excitatory or inhibitory based on their strong positive or strong negative values.
In [28]:
if chosen_filter == None:
chosen_filter = 179
In [29]:
from tensorflow.keras.applications import VGG19
import numpy as np
import matplotlib.pyplot as plt
# Load the VGG19 model
model = VGG19(weights='imagenet')
# Choose a layer to analyze
#layer_name = 'block5_conv1'
layer_name = 'block5_conv2'
layer = model.get_layer(name=layer_name)
# Extract the filter weights from the chosen layer
filters, biases = layer.get_weights()
print(f"Shape of filters in {layer_name}: {filters.shape}")
# Select a single multi-channel filter
single_multi_channel_filter = filters[:, :, :, chosen_filter] # Shape (3, 3, 512)
Shape of filters in block5_conv2: (3, 3, 512, 512)
In [30]:
# Set up the plot dimensions
n_filters = filters.shape[3]
n_channels = filters.shape[2]
size = int(np.ceil(np.sqrt(n_channels))) # for a square grid
# Visualize each channel of each filter
for filter_idx in range(n_filters):
fig, axes = plt.subplots(size, size, figsize=(12, 12))
for i in range(n_channels):
ax = axes.flatten()[i]
channel_filter = filters[:, :, i, filter_idx] # Shape: (3, 3)
ax.imshow(channel_filter, aspect='auto', cmap='gray')
ax.axis('off')
plt.show()
if filter_idx == 0: # just show the first filter for demonstration
break
In [31]:
# Compute the L2 norm for each 3x3 filter within this multi-channel filter
l2_norms = np.linalg.norm(single_multi_channel_filter, axis=(0, 1))
# Find the indices of the ten strongest 3x3 filters
top_ten_indices = np.argsort(l2_norms)[-10:]
# Visualize these top ten 3x3 filters
fig, axes = plt.subplots(1, 10, figsize=(20, 2))
for i, idx in enumerate(top_ten_indices):
# Extract each 3x3 filter
single_filter = single_multi_channel_filter[:, :, idx]
axes[i].imshow(single_filter, cmap='gray')
axes[i].axis('off')
axes[i].set_title(f"Channel {idx}")
plt.show()
print("Top 10 strongest channels in the selected multi-channel filter:")
for idx in top_ten_indices:
single_channel_filter = single_multi_channel_filter[:, :, idx]
# Count the number of positive and negative weights in the single channel filter
# counts how many weights (or values) in the single_channel_filter are greater than zero. It does this by creating a boolean array where each element is True if the corresponding weight in single_channel_filter is greater than zero and False otherwise.
num_positive = np.sum(single_channel_filter > 0)
num_negative = np.sum(single_channel_filter < 0)
# Get the L2 norm strength for the current channel
strength = l2_norms[idx]
# Determine if the channel filter is mostly inhibitory or excitatory based on the magnitude
if num_negative > num_positive:
print(f"Channel {idx} is mostly inhibitory (Difference: {num_positive - num_negative}, L2 Norm (Channel Filter Strength): {strength})")
else:
print(f"Channel {idx} is mostly excitatory (Difference: {num_positive - num_negative}, L2 Norm (Channel Filter Strength): {strength})")
Top 10 strongest channels in the selected multi-channel filter: Channel 314 is mostly excitatory (Difference: 9, L2 Norm (Channel Filter Strength): 0.048861004412174225) Channel 505 is mostly excitatory (Difference: 9, L2 Norm (Channel Filter Strength): 0.04975984990596771) Channel 246 is mostly excitatory (Difference: 5, L2 Norm (Channel Filter Strength): 0.050983574241399765) Channel 62 is mostly inhibitory (Difference: -9, L2 Norm (Channel Filter Strength): 0.053933966904878616) Channel 266 is mostly excitatory (Difference: 3, L2 Norm (Channel Filter Strength): 0.057091664522886276) Channel 133 is mostly excitatory (Difference: 9, L2 Norm (Channel Filter Strength): 0.05907253175973892) Channel 117 is mostly inhibitory (Difference: -9, L2 Norm (Channel Filter Strength): 0.05968699976801872) Channel 271 is mostly inhibitory (Difference: -9, L2 Norm (Channel Filter Strength): 0.06347174942493439) Channel 294 is mostly excitatory (Difference: 9, L2 Norm (Channel Filter Strength): 0.06414642184972763) Channel 162 is mostly inhibitory (Difference: -9, L2 Norm (Channel Filter Strength): 0.06482560932636261)
Summary:¶
Our analysis shows that for this task, choosing filter 179 in the block5_conv2 layer of VGG19, has the following strongest channels: 314, 505, 246, 62, 266, 133, 117, 271, 294, 162
4.0 Image Gradient Visualization¶
[4 points]
For each of the ten chosen single channels of the filter, use image gradient techniques to visualize what each of these filters is most excited by (that is, what image maximally excites each of these filters?). This is a similar analysis to the first step in this rubric, but now isolating the activations the layer preceding your chosen filter. This should only be completed for the ten most influential filters.¶
- Use these visualizations, along with the circuit weights you just discovered to try and explain how this particular circuit works. An example of this visualization style can be seen here:¶
https://storage.googleapis.com/distill-circuits/inceptionv1-weight-explorer/mixed3b_379.html
- Try to define the properties of this circuit using vocabulary from https://distill.pub/2020/circuits/zoom-in/Links to an external site. (such as determining if this is polysemantic, pose-invariant, etc.)¶
- Relate your visualizations back to your original hypothesis about what this filter is extracting. Does it support or refute your hypothesis? Why?¶
Notes:
Use Gradient techniques for this
Start at the output activation, figure out the channels of the filter that are most important, then use those to index into the previous layer & excite those in the same way with image gradient techniques (looking for strong weights) - later layers are sparse and give the biggest indicator of what is activating
Process:
- We've chosen block5_conv2, which has 512 filters of shape 512x3x3
- We've chosen output filter 179 of block5_conv2, which has 512 channels of shape 3x3
- We've chosen input activation channels 314, 505, 246, 62, 266, 133, 117, 271, 294, 162 which have the strongest weights
We are using the same image gradient approach as above, but we are extracting the activations from the previous layer, which is block5_conv1, and the filters associated with the channels from block5_conv2.
In [32]:
#Using gradient ascent
def generate_pattern2(layer_name, prev_layer_name, filter_index, chan_in, size=150):
# Build a model that outputs the activation
# of the nth filter of the layer considered.
#layer_output = model.get_layer(layer_name).output
prev_layer_output = model.get_layer(prev_layer_name).output
# Isolate the output
#new_model = models.Model(inputs=model.input, outputs=layer_output)
# Using the previous model structure
prev_model = models.Model(inputs=model.input,outputs=prev_layer_output)
# We start from a gray image with some uniform noise
input_img_data = np.random.random((1, size, size, 3)) * 20 + 128.
# Capturing activations from previous layer and using channel index on those
#activations = prev_model.predict(input_img_data) # Predict on block5_conv1
#act1 = activations[0]
#filter_output = activations[0, :, :, chan_in]
I_start = tf.Variable(input_img_data, name='image_var', dtype = 'float64')
I = preprocess_input(I_start) # only process once
# Run gradient ascent for 40 steps
eta = 1.
for i in range(40):
with tf.GradientTape(watch_accessed_variables=False) as tape:
tape.watch(I)
# get variable to maximize
model_vals = prev_model(I)
filter_output = tf.reduce_mean(model_vals[:, :, :, chan_in])
# Compute the gradient of the input picture w.r.t. this loss
# add this operation input to maximize
grad_fn = tape.gradient(filter_output, I)
# Normalization trick: we normalize the gradient
grad_fn /= (tf.sqrt(tf.reduce_mean(tf.square(grad_fn))) + 1e-5) # mean L2 norm
I += grad_fn * eta # one iteration of maximizing
# return the numpy matrix so we can visualize
img = I.numpy()
return prepare_image_for_display(img, norm_type='std')
In [33]:
layer_name = 'block5_conv2'
prev_layer_name = 'block5_conv1'
filter_index_chosen = 179
chan_strong = [314, 505, 246, 62, 266, 133, 117, 271, 294, 162]
for chan_in in chan_strong:
size = 224
margin = 5
# This is an empty (black) image where we will store our results.
results = np.zeros((8 * size + 7 * margin, 8 * size + 7 * margin, 3)).astype('uint8')
filter_img = generate_pattern2(layer_name, prev_layer_name, filter_index_chosen, chan_in, size=size)
results = filter_img
# Display the results grid
print('Previous Layer Activations: Block 5, Conv 1, Channel', chan_in)
plt.figure(figsize=(5, 5))
plt.imshow(results)
#plt.title('Block 5, Conv 1, Filter ', filter_index_chosen, 'Channel', chan_in)
plt.show()
Previous Layer Activations: Block 5, Conv 1, Channel 314
Previous Layer Activations: Block 5, Conv 1, Channel 505
Previous Layer Activations: Block 5, Conv 1, Channel 246
Previous Layer Activations: Block 5, Conv 1, Channel 62
Previous Layer Activations: Block 5, Conv 1, Channel 266
Previous Layer Activations: Block 5, Conv 1, Channel 133
Previous Layer Activations: Block 5, Conv 1, Channel 117
Previous Layer Activations: Block 5, Conv 1, Channel 271
Previous Layer Activations: Block 5, Conv 1, Channel 294
Previous Layer Activations: Block 5, Conv 1, Channel 162
In [35]:
grid_rows = 2
grid_cols = 5
size = 224
margin = 5
results_height = grid_rows * size + (grid_rows - 1) * margin
results_width = grid_cols * size + (grid_cols - 1) * margin
results = np.zeros((results_height, results_width, 3), dtype='uint8')
for i, chan_in in enumerate(chan_strong):
filter_img = generate_pattern2(layer_name, prev_layer_name, filter_index_chosen, chan_in, size=size)
row = i // grid_cols
col = i % grid_cols
row_start = row * (size + margin)
col_start = col * (size + margin)
results[row_start:row_start + size, col_start:col_start + size, :] = filter_img
plt.figure(figsize=(20, 8))
plt.imshow(results)
# plt.title(f'Activations for layer {layer_name}, previous layer {prev_layer_name}, filter index {filter_index_chosen}')
plt.axis('off')
plt.show()
Analyzing the circuit¶
In accordance with our hypothesis, the channels that most excited our chosen filter indicate a strong affinity for a combination of circular and wavy figures. One of the selected channels appears extremely floral, which would not have had a particularly successful impact in identifying any of the main subjects in our dataset. On the other hand, we believe a vast majority of the channels visualized above show a strong correlation betweeen the eyes and stripes that can be found on mammals such as giraffes and zebras.
When comparing the channels visualized in this section to the single visualization of filter 179 in Section 2.0 above, we noticed a pattern of curves, spirals, and distinct floral shapes. This could indicate that this filter is particularly good at identifying shapes including eyes, flowers, and other patterns.
Summary¶
In this lab, we analyzed the inner workings of the multi-layer, multi-channel CNN VGG19. We found both numeric agreement and visual agreement between layer activations and filter channel weights.
In [ ]: